Simplify (1/(x^3))÷(5/(x^2))

$\frac{1}{x^{3}} \div \frac{5}{x^{2}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{x^{3}} \cdot \frac{x^{2}}{5}$

Combine.

$\frac{1 x^{2}}{x^{3} \cdot 5}$

Cancel the common factor of $x^{2}$ and $x^{3}$ .

Factor $x^{2}$ out of $1 x^{2}$ .

$\frac{x^{2} \cdot 1}{x^{3} \cdot 5}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{3} \cdot 5$ .

$\frac{x^{2} \cdot 1}{x^{2} (x \cdot 5)}$

Cancel the common factor.

$\frac{x^{2} \cdot 1}{x^{2} (x \cdot 5)}$

Rewrite the expression.

$\frac{1}{x \cdot 5}$

Move $5$ to the left of $x$ .

$\frac{1}{5 x}$